\[\theta\left(z_{1},z_{2}\middle|\begin{bmatrix}i&-\tfrac{1}{2}\\
-\tfrac{1}{2}&i\end{bmatrix}\right)=\sum_{n_{1}=-\infty}^{\infty}\sum_{n_{2}=-%
\infty}^{\infty}e^{-\pi(n_{1}^{2}+n_{2}^{2})}e^{-i\pi n_{1}n_{2}}e^{2\pi i(n_{%
1}z_{1}+n_{2}z_{2})}.\]